"The mouse is in trouble, because the owl is quiet."
Translation:Hiiri on pulassa, koska pöllö on hiljaa.
It means the owl is not making any sounds currently. "Hiljainen" would mean that it's never that loud to begin with, or if there's a context to it: there might be something wrong with the owl if it's normally loud but not right now.
About places you can only say "hiljainen", living things can be either hiljaa or hiljainen.